多尺度多孔介质的有效气体渗透率研究
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摘要
多孔介质的气体渗透率对于油气资源、微机电系统、燃料电池、生物组织、纤维以及复合材料等具有重要的理论和实际意义。然而,多孔介质内孔隙结构和连通性十分复杂,孔隙尺度范围极广,从常规尺度到微纳米尺度形成了多尺度并存的物理结构,气体在多尺度孔隙结构中的流动涉及多种输运机制。本文基于分形几何理论,建立了多尺度多孔介质气体渗流的物理和数学模型,理论推导了多尺度多孔介质的有效气体渗透率,研究了多孔介质的微结构参数对于有效气体渗透率的定量影响。结果表明,多尺度多孔介质的气体输运过程不仅依赖于介质的微细结构还依赖于气体属性,微纳尺度孔隙的气体滑移效应显著。
Gas permeability of porous media is of great theoretical and practical importance for oil and gas resources, micro-electro-mechanical systems, fuel cells, biological tissues, fibrous and composite materials etc. However, the pore structure and its connectivity in porous media are very complex, and the multi-scale pores with size from normal to micro/nano scale coexist. Therefore,gas flow thorough multi-scale porous media involves several different transport mechanisms. In this work, a physical and mathematical model is developed to study the gas flow thorough multi-scale porous media based on fractal geometry. The effective gas permeability is derived, and the effect of structural parameters of porous media on the effective gas permeability is analyzed accordingly. The present results indicate that gas flow in multi-scale porous media depends on both the microstructure and gas property, and the gas slippage effect in micro-and nano-scale pores is significant.
Gas permeability of porous media is of great theoretical and practical importance for oil and gas resources, micro-electro-mechanical systems, fuel cells, biological tissues, fibrous and composite materials etc. However, the pore structure and its connectivity in porous media are very complex, and the multi-scale pores with size from normal to micro/nano scale coexist. Therefore,gas flow thorough multi-scale porous media involves several different transport mechanisms. In this work, a physical and mathematical model is developed to study the gas flow thorough multi-scale porous media based on fractal geometry. The effective gas permeability is derived, and the effect of structural parameters of porous media on the effective gas permeability is analyzed accordingly. The present results indicate that gas flow in multi-scale porous media depends on both the microstructure and gas property, and the gas slippage effect in micro-and nano-scale pores is significant.
引文
[1]郁伯铭,徐鹏,邹明清,等.分形多孔介质输运物理[M].北京:科学出版社,2014:1-18YU Boming, XU Peng, ZOU Mingqing, et al. Fractal Physical Transport in Porous Media[M]. Beijing:Science Press, 2014:1-18
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[3] TANG Guihua, TAO Wenquan, HE Yaling. Gas Slippage Effect on Microscale Porous Flow Using the Lattice Boltzmann Method[J]. Physical Review E, 2005, 72:056301
[4] Javadpour F, Fisher D, Unsworth M. Nanoscale Gas Flow in Shale Gas Sediments[J]. Journal of Canadian Petroleum Technology, 2007, 46:55-61
[5] Pant L M, Mitra S K, Secanell M. Absolute Permeability and Knudsen Diffusivity Measurements in PEMFC Gas Diffusion Layers and Micro Porous Layers[J]. Journal of Power Sources, 2012, 206:153-160
[6] LIU Qixin, JIANG Peixue, XIANG Heng. Experimental and Molecular Dynamics Study of Gas Flow Characteristics in Nanopores[J]. Chinese Science Bulletin, 2012,57(13):1488-1493
[7] SHOU Dahua, FAN Jintu, MEI Maofei, et al. An Analytical Model for Gas Diffusion Though Nanoscale andMicroscale Fibrous Media[J]. Microfluid Nanofluid, 2014,16(1/2):381-389
[8] ZHANG Lei, KANG Qinjun, YAO Jun, et al. Pore Scale Simulation of Liquid and Gas Two-Phase Flow Based on Digital Core Technology[J]. Science China Technological Sciences, 2015, 58:1375-1384
[9] XU Peng, QIU Shuxia, CAI Jianchao, et al. A Noverl Analytical Solution for Gas Diffusion in Multi-Scale Fuel Cell Porous Media[J]. Journal of Power Sources, 2017,362:73-79
[10] YU Boming. Analysis of Flow in Fractal Porous Media[J]. Applied Mechanics Reviews, 2008, 61:050801
[11] XU Peng, QIU Shuxia, YU Boming, et al. Prediction of Relative Permeability in Unsaturated Porous Media with a Fractal Approach[J]. International Journal of Heat and Mass Transfer, 2013, 64:829-837
[12] XU Peng. A Discussion on Fractal Models for Transport Physics of Porous Media[J]. Fractals, 2015, 23:1530001
[13] LI Cuihong, XU Peng, QIU Shuxia, et al. The Gas Effective Permeability of Porous Media with Klinkenberg Effect[J]. Journal of Natural Gas Science and Engineering, 2016,34:534-540
[14] XU Peng, LI Cuihong, QIU Shuxia, et al. A Fractal Network Model for Fractured Porous Media[J]. Fractals,2016, 24(02):1650018
[15] XU Peng, LIU Haicheng, SASMITO A P, et al. Effective Permeability of Fractured Porous Media with Fractal Dual-Porosity Model[J]. Fractals, 2017, 25(4):1740014
[16] Beskok A, Karniadakis G E. Report:a Model for Flows in Channels, Pipes, and Ducts At Micro and Nano Scales[J]. Microscale Thermophysical Engineering, 1999, 3(1):43-77
[17] Klinkenberg L J. The Permeability of Porous Media to Liquid and Gases[C]//Drilling and Production Practice.New York:American Petroleum Institute, 1941:200-213
[18] Florence F A, Rushing J A, Newsham K E, et al. Improved Permeability Prediction Relations for Low Permeability Sands[C]//Rocky Mountain Oil&Gas Technology Symposium. Denver:Society of Petroleum Engineers,2007:10795
[2] Roy S, Raju R. Modeling Gas Flow Through Microchannels and Nanopores[J]. Journal of Applied Physics, 2003,93(8):4870-4879
[3] TANG Guihua, TAO Wenquan, HE Yaling. Gas Slippage Effect on Microscale Porous Flow Using the Lattice Boltzmann Method[J]. Physical Review E, 2005, 72:056301
[4] Javadpour F, Fisher D, Unsworth M. Nanoscale Gas Flow in Shale Gas Sediments[J]. Journal of Canadian Petroleum Technology, 2007, 46:55-61
[5] Pant L M, Mitra S K, Secanell M. Absolute Permeability and Knudsen Diffusivity Measurements in PEMFC Gas Diffusion Layers and Micro Porous Layers[J]. Journal of Power Sources, 2012, 206:153-160
[6] LIU Qixin, JIANG Peixue, XIANG Heng. Experimental and Molecular Dynamics Study of Gas Flow Characteristics in Nanopores[J]. Chinese Science Bulletin, 2012,57(13):1488-1493
[7] SHOU Dahua, FAN Jintu, MEI Maofei, et al. An Analytical Model for Gas Diffusion Though Nanoscale andMicroscale Fibrous Media[J]. Microfluid Nanofluid, 2014,16(1/2):381-389
[8] ZHANG Lei, KANG Qinjun, YAO Jun, et al. Pore Scale Simulation of Liquid and Gas Two-Phase Flow Based on Digital Core Technology[J]. Science China Technological Sciences, 2015, 58:1375-1384
[9] XU Peng, QIU Shuxia, CAI Jianchao, et al. A Noverl Analytical Solution for Gas Diffusion in Multi-Scale Fuel Cell Porous Media[J]. Journal of Power Sources, 2017,362:73-79
[10] YU Boming. Analysis of Flow in Fractal Porous Media[J]. Applied Mechanics Reviews, 2008, 61:050801
[11] XU Peng, QIU Shuxia, YU Boming, et al. Prediction of Relative Permeability in Unsaturated Porous Media with a Fractal Approach[J]. International Journal of Heat and Mass Transfer, 2013, 64:829-837
[12] XU Peng. A Discussion on Fractal Models for Transport Physics of Porous Media[J]. Fractals, 2015, 23:1530001
[13] LI Cuihong, XU Peng, QIU Shuxia, et al. The Gas Effective Permeability of Porous Media with Klinkenberg Effect[J]. Journal of Natural Gas Science and Engineering, 2016,34:534-540
[14] XU Peng, LI Cuihong, QIU Shuxia, et al. A Fractal Network Model for Fractured Porous Media[J]. Fractals,2016, 24(02):1650018
[15] XU Peng, LIU Haicheng, SASMITO A P, et al. Effective Permeability of Fractured Porous Media with Fractal Dual-Porosity Model[J]. Fractals, 2017, 25(4):1740014
[16] Beskok A, Karniadakis G E. Report:a Model for Flows in Channels, Pipes, and Ducts At Micro and Nano Scales[J]. Microscale Thermophysical Engineering, 1999, 3(1):43-77
[17] Klinkenberg L J. The Permeability of Porous Media to Liquid and Gases[C]//Drilling and Production Practice.New York:American Petroleum Institute, 1941:200-213
[18] Florence F A, Rushing J A, Newsham K E, et al. Improved Permeability Prediction Relations for Low Permeability Sands[C]//Rocky Mountain Oil&Gas Technology Symposium. Denver:Society of Petroleum Engineers,2007:10795